suppose $a(x)$ and $b(x)$ have degree smaller than $n$. If $a(c)=b(c)$ for $n$ values of $c$, prove $a(x)=b(x)$

Question

Suppose $a(x)$ and $b(x)$ have degree smaller than $n$. If $a(c)=b(c)$ for $n$ values of $c$, prove $a(x)=b(x)$

I don't understand how there is $n$ values of $c$ but the polynomials are of degree less than $n$ and so I don't know how to go about the proof. Any hints will help!

Answer 1

Hint: Consider the $h(x)=a(x)-b(x)$ and use the algebra's fundamental theorem.

Answer 2

Hint: Consider $p(x)=a(x)-b(x)$.